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SOLUTIONS
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Functions
- Cycles
- FindPermutation
- InversePermutation
- Ordering
- Part
- PermutationCycles
- PermutationCyclesQ
- PermutationLength
- PermutationList
- PermutationListQ
- PermutationMax
- PermutationMin
- PermutationOrder
- PermutationPower
- PermutationProduct
- PermutationReplace
- Permutations
- PermutationSupport
- Permute
- RandomPermutation
- RandomSample
- Signature
- Sort
- Tutorials
Permutations
Permutations are among the most basic elements of discrete mathematics. They can be used to represent discrete groups of transformations and in particular play a key role in the description of the concept of symmetry. Mathematica 8 provides new functionality to work with permutations, both in list and cyclic form, and allows their action on generic expressions in a variety of ways.
ReferenceReference
Permutation Representation
Cycles — cyclic permutation representation
PermutationCyclesQ — test validity
PermutationCycles — convert to cyclic representation
PermutationList — convert to permutation list representation
PermutationListQ — test validity
RandomPermutation — random generation of permutations
Permutation Operations
PermutationReplace — standard action of a permutation on other objects
PermutationProduct ▪ InversePermutation ▪ PermutationPower
Permute — permute arguments of an expression
FindPermutation — permutation linking two expressions
Permutations — all permutations of arguments of an expression
Permutation Properties
PermutationOrder — order of a permutation
PermutationSupport ▪ PermutationLength ▪ PermutationMin ▪ PermutationMax
Permutation Lists
Sort — return identity permutation list
Part — product of permutation lists
Ordering — inverse of a permutation list
Signature — signature of a permutation list
RandomSample — random generation of permutation lists
